The injection sets provided in [1]}, [2]} for the combined O1+O2+O3 sensitivity and O3 sensitivity respectively contain 41,972 and 81,117 simulated events which pass our detection threshold. As expected, the use of more samples reduces the uncertainty in the computed \(p_{\rm det}\)  estimate, and is reflected by the distribution of variances in \(\ln \mathcal {L}\) , as shown in Figure REF . We drastically reduce the variances in the log likelihood estimates by using our own injection set which contains 911,386 injections passing our detection threshold.
